Coefficient Systems on the Bruhat-tits Building and Pro-p Iwahori-hecke Modules

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Let G be the group of rational points of a split connected reductive group over a non-Archimedean local field of residue characteristic p, says Kohlhaase, and let I be a pro-p Iwahori subgroup of G and let R be a commutative quasi-Frobenius ring. So, if H = R[I\G/I] denotes the pro-p Iwahori-Hecke algebra of G over R, he clarifies the relation between the category of H-modules and the category of G-equivariant coefficient systems on the semisimple Bruhat-Tits building of G. Annotation ©2022 Ringgold, Inc., Portland, OR (protoview.com) Cover Title page Introduction Chapter 1. A reminder on the Bruhat-Tits building 1.1. Stabilizers and Bruhat decompositions 1.2. Hecke algebras Chapter 2. Coefficient systems 2.1. Coefficient systems and diagrams 2.2. Acyclic coefficient systems on the standard apartment Chapter 3. The equivalence of categories 3.1. Representations and Hecke modules of stabilizer groups 3.2. Coefficient systems and pro-𝑝 Iwahori-Hecke modules Chapter 4. Applications to representation theory 4.1. Homology in degree zero 4.2. Homotopy categories and their localizations 4.3. The functor to generalized (𝜑,Γ)-modules Bibliography Back Cover